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Chords of ennealimnic

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Below are listed the dyadic chords of 11-limit ennealimnic temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are labeled swetismic, 441/440 werckismic, and by 243/242 rastmic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove.

The normal mapping for ennealimnic is enn = [<9 1 1 12 -2|, <0 2 3 2 5|]. From this we may derive a val v = enn[1] + 100 enn[2] = <9 201 301 212 498| which we may use to sort and normalize the chords of ennealimmic. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v, and the nnextw column gives a transversal which tempers to the chord by ennealimmic tempering. Finally, the Graham complexity is listed in the last column.

Ennealimmic has MOS of size 18, 27, 45 and 72. It may be seen that the 18 note MOS has some triads and tetrads, and 27 considerably more.

Triads

Number
 Chord
 Transversal
 Type
 Complexity
1
 0-7-96
 1-12/7-11/9
 swetismic
 9
2
 0-2-98
 1-7/6-10/7
 swetismic
 9
3
 0-7-98
 1-12/7-10/7
 otonal
 9
4
 0-96-98
 1-11/9-10/7
 swetismic
 9
5
 0-2-100
 1-7/6-5/3
 otonal
 9
6
 0-98-100
 1-10/7-5/3
 utonal
 9
7
 0-7-188
 1-12/7-11/10
 swetismic
 18
8
 0-96-188
 1-11/9-11/10
 utonal
 18
9
 0-101-188
 1-9/5-11/10
 otonal
 18
10
 0-2-190
 1-7/6-9/7
 swetismic
 18
11
 0-7-190
 1-12/7-9/7
 otonal
 18
12
 0-98-190
 1-10/7-9/7
 otonal
 18
13
 0-101-190
 1-9/5-9/7
 utonal
 18
14
 0-188-190
 1-11/10-9/7
 swetismic
 18
15
 0-2-192
 1-7/6-3/2
 otonal
 18
16
 0-7-192
 1-12/7-3/2
 utonal
 18
17
 0-96-192
 1-11/9-3/2
 rastmic
 18
18
 0-100-192
 1-5/3-3/2
 otonal
 18
19
 0-101-192
 1-9/5-3/2
 utonal
 18
20
 0-190-192
 1-9/7-3/2
 utonal
 18
21
 0-2-194
 1-7/6-7/4
 utonal
 18
22
 0-96-194
 1-11/9-7/4
 werckismic
 18
23
 0-98-194
 1-10/7-7/4
 werckismic
 18
24
 0-192-194
 1-3/2-7/4
 otonal
 18
25
 0-98-283
 1-10/7-5/4
 utonal
 27
26
 0-100-283
 1-5/3-5/4
 utonal
 27
27
 0-192-283
 1-3/2-5/4
 otonal
 27
28
 0-194-283
 1-7/4-5/4
 otonal
 27
29
 0-7-286
 1-12/7-11/7
 otonal
 27
30
 0-96-286
 1-11/9-11/7
 utonal
 27
31
 0-98-286
 1-10/7-11/7
 otonal
 27
32
 0-101-286
 1-9/5-11/7
 werckismic
 27
33
 0-188-286
 1-11/10-11/7
 utonal
 27
34
 0-190-286
 1-9/7-11/7
 otonal
 27
35
 0-194-286
 1-7/4-11/7
 werckismic
 27
36
 0-2-288
 1-7/6-11/6
 otonal
 27
37
 0-96-288
 1-11/9-11/6
 utonal
 27
38
 0-98-288
 1-10/7-11/6
 swetismic
 27
39
 0-100-288
 1-5/3-11/6
 otonal
 27
40
 0-188-288
 1-11/10-11/6
 utonal
 27
41
 0-190-288
 1-9/7-11/6
 swetismic
 27
42
 0-192-288
 1-3/2-11/6
 otonal
 27
43
 0-286-288
 1-11/7-11/6
 utonal
 27
44
 0-96-375
 1-11/9-9/8
 rastmic
 36
45
 0-98-375
 1-10/7-9/8
 werckismic
 36
46
 0-101-375
 1-9/5-9/8
 utonal
 36
47
 0-190-375
 1-9/7-9/8
 utonal
 36
48
 0-192-375
 1-3/2-9/8
 ambitonal
 36
49
 0-194-375
 1-7/4-9/8
 otonal
 36
50
 0-283-375
 1-5/4-9/8
 otonal
 36
51
 0-286-375
 1-11/7-9/8
 werckismic
 36
52
 0-288-375
 1-11/6-9/8
 rastmic
 36
53
 0-96-471
 1-11/9-11/8
 utonal
 45
54
 0-188-471
 1-11/10-11/8
 utonal
 45
55
 0-192-471
 1-3/2-11/8
 otonal
 45
56
 0-194-471
 1-7/4-11/8
 otonal
 45
57
 0-283-471
 1-5/4-11/8
 otonal
 45
58
 0-286-471
 1-11/7-11/8
 utonal
 45
59
 0-288-471
 1-11/6-11/8
 utonal
 45
60
 0-375-471
 1-9/8-11/8
 otonal
 45

Tetrads

Number
 Chord
 Transversal
 Type
 Complexity
1
 0-7-96-98
 1-12/7-11/9-10/7
 swetismic
 9
2
 0-2-98-100
 1-7/6-10/7-5/3
 swetismic
 9
3
 0-7-96-188
 1-12/7-11/9-11/10
 swetismic
 18
4
 0-2-98-190
 1-7/6-10/7-9/7
 swetismic
 18
5
 0-7-98-190
 1-12/7-10/7-9/7
 otonal
 18
6
 0-7-188-190
 1-12/7-11/10-9/7
 swetismic
 18
7
 0-101-188-190
 1-9/5-11/10-9/7
 swetismic
 18
8
 0-7-96-192
 1-12/7-11/9-3/2
 jove
 18
9
 0-2-100-192
 1-7/6-5/3-3/2
 otonal
 18
10
 0-2-190-192
 1-7/6-9/7-3/2
 swetismic
 18
11
 0-7-190-192
 1-12/7-9/7-3/2
 ambitonal
 18
12
 0-101-190-192
 1-9/5-9/7-3/2
 utonal
 18
13
 0-2-98-194
 1-7/6-10/7-7/4
 jove
 18
14
 0-96-98-194
 1-11/9-10/7-7/4
 jove
 18
15
 0-2-192-194
 1-7/6-3/2-7/4
 ambitonal
 18
16
 0-96-192-194
 1-11/9-3/2-7/4
 jove
 18
17
 0-98-100-283
 1-10/7-5/3-5/4
 utonal
 27
18
 0-100-192-283
 1-5/3-3/2-5/4
 ambitonal
 27
19
 0-98-194-283
 1-10/7-7/4-5/4
 werckismic
 27
20
 0-192-194-283
 1-3/2-7/4-5/4
 otonal
 27
21
 0-7-96-286
 1-12/7-11/9-11/7
 swetismic
 27
22
 0-7-98-286
 1-12/7-10/7-11/7
 otonal
 27
23
 0-96-98-286
 1-11/9-10/7-11/7
 swetismic
 27
24
 0-7-188-286
 1-12/7-11/10-11/7
 swetismic
 27
25
 0-96-188-286
 1-11/9-11/10-11/7
 utonal
 27
26
 0-101-188-286
 1-9/5-11/10-11/7
 werckismic
 27
27
 0-7-190-286
 1-12/7-9/7-11/7
 otonal
 27
28
 0-98-190-286
 1-10/7-9/7-11/7
 otonal
 27
29
 0-101-190-286
 1-9/5-9/7-11/7
 werckismic
 27
30
 0-188-190-286
 1-11/10-9/7-11/7
 swetismic
 27
31
 0-96-194-286
 1-11/9-7/4-11/7
 werckismic
 27
32
 0-98-194-286
 1-10/7-7/4-11/7
 werckismic
 27
33
 0-2-98-288
 1-7/6-10/7-11/6
 swetismic
 27
34
 0-96-98-288
 1-11/9-10/7-11/6
 swetismic
 27
35
 0-2-100-288
 1-7/6-5/3-11/6
 otonal
 27
36
 0-98-100-288
 1-10/7-5/3-11/6
 swetismic
 27
37
 0-96-188-288
 1-11/9-11/10-11/6
 utonal
 27
38
 0-2-190-288
 1-7/6-9/7-11/6
 swetismic
 27
39
 0-98-190-288
 1-10/7-9/7-11/6
 swetismic
 27
40
 0-188-190-288
 1-11/10-9/7-11/6
 swetismic
 27
41
 0-2-192-288
 1-7/6-3/2-11/6
 otonal
 27
42
 0-96-192-288
 1-11/9-3/2-11/6
 rastmic
 27
43
 0-100-192-288
 1-5/3-3/2-11/6
 otonal
 27
44
 0-190-192-288
 1-9/7-3/2-11/6
 swetismic
 27
45
 0-96-286-288
 1-11/9-11/7-11/6
 utonal
 27
46
 0-98-286-288
 1-10/7-11/7-11/6
 swetismic
 27
47
 0-188-286-288
 1-11/10-11/7-11/6
 utonal
 27
48
 0-190-286-288
 1-9/7-11/7-11/6
 swetismic
 27
49
 0-96-98-375
 1-11/9-10/7-9/8
 jove
 36
50
 0-98-190-375
 1-10/7-9/7-9/8
 werckismic
 36
51
 0-101-190-375
 1-9/5-9/7-9/8
 utonal
 36
52
 0-96-192-375
 1-11/9-3/2-9/8
 rastmic
 36
53
 0-101-192-375
 1-9/5-3/2-9/8
 utonal
 36
54
 0-190-192-375
 1-9/7-3/2-9/8
 utonal
 36
55
 0-96-194-375
 1-11/9-7/4-9/8
 jove
 36
56
 0-98-194-375
 1-10/7-7/4-9/8
 werckismic
 36
57
 0-192-194-375
 1-3/2-7/4-9/8
 otonal
 36
58
 0-98-283-375
 1-10/7-5/4-9/8
 werckismic
 36
59
 0-192-283-375
 1-3/2-5/4-9/8
 otonal
 36
60
 0-194-283-375
 1-7/4-5/4-9/8
 otonal
 36
61
 0-96-286-375
 1-11/9-11/7-9/8
 jove
 36
62
 0-98-286-375
 1-10/7-11/7-9/8
 werckismic
 36
63
 0-101-286-375
 1-9/5-11/7-9/8
 werckismic
 36
64
 0-190-286-375
 1-9/7-11/7-9/8
 werckismic
 36
65
 0-194-286-375
 1-7/4-11/7-9/8
 werckismic
 36
66
 0-96-288-375
 1-11/9-11/6-9/8
 rastmic
 36
67
 0-98-288-375
 1-10/7-11/6-9/8
 jove
 36
68
 0-190-288-375
 1-9/7-11/6-9/8
 jove
 36
69
 0-192-288-375
 1-3/2-11/6-9/8
 rastmic
 36
70
 0-286-288-375
 1-11/7-11/6-9/8
 jove
 36
71
 0-96-188-471
 1-11/9-11/10-11/8
 utonal
 45
72
 0-96-192-471
 1-11/9-3/2-11/8
 rastmic
 45
73
 0-96-194-471
 1-11/9-7/4-11/8
 werckismic
 45
74
 0-192-194-471
 1-3/2-7/4-11/8
 otonal
 45
75
 0-192-283-471
 1-3/2-5/4-11/8
 otonal
 45
76
 0-194-283-471
 1-7/4-5/4-11/8
 otonal
 45
77
 0-96-286-471
 1-11/9-11/7-11/8
 utonal
 45
78
 0-188-286-471
 1-11/10-11/7-11/8
 utonal
 45
79
 0-194-286-471
 1-7/4-11/7-11/8
 werckismic
 45
80
 0-96-288-471
 1-11/9-11/6-11/8
 utonal
 45
81
 0-188-288-471
 1-11/10-11/6-11/8
 utonal
 45
82
 0-192-288-471
 1-3/2-11/6-11/8
 ambitonal
 45
83
 0-286-288-471
 1-11/7-11/6-11/8
 utonal
 45
84
 0-96-375-471
 1-11/9-9/8-11/8
 rastmic
 45
85
 0-192-375-471
 1-3/2-9/8-11/8
 otonal
 45
86
 0-194-375-471
 1-7/4-9/8-11/8
 otonal
 45
87
 0-283-375-471
 1-5/4-9/8-11/8
 otonal
 45
88
 0-286-375-471
 1-11/7-9/8-11/8
 werckismic
 45
89
 0-288-375-471
 1-11/6-9/8-11/8
 rastmic
 45

Pentads

Number
 Chord
 Transversal
 Type
 Complexity
1
 0-7-96-98-286
 1-12/7-11/9-10/7-11/7
 swetismic
 27
2
 0-7-96-188-286
 1-12/7-11/9-11/10-11/7
 swetismic
 27
3
 0-7-98-190-286
 1-12/7-10/7-9/7-11/7
 otonal
 27
4
 0-7-188-190-286
 1-12/7-11/10-9/7-11/7
 swetismic
 27
5
 0-101-188-190-286
 1-9/5-11/10-9/7-11/7
 jove
 27
6
 0-96-98-194-286
 1-11/9-10/7-7/4-11/7
 jove
 27
7
 0-2-98-100-288
 1-7/6-10/7-5/3-11/6
 swetismic
 27
8
 0-2-98-190-288
 1-7/6-10/7-9/7-11/6
 swetismic
 27
9
 0-2-100-192-288
 1-7/6-5/3-3/2-11/6
 otonal
 27
10
 0-2-190-192-288
 1-7/6-9/7-3/2-11/6
 swetismic
 27
11
 0-96-98-286-288
 1-11/9-10/7-11/7-11/6
 swetismic
 27
12
 0-96-188-286-288
 1-11/9-11/10-11/7-11/6
 utonal
 27
13
 0-98-190-286-288
 1-10/7-9/7-11/7-11/6
 swetismic
 27
14
 0-188-190-286-288
 1-11/10-9/7-11/7-11/6
 swetismic
 27
15
 0-101-190-192-375
 1-9/5-9/7-3/2-9/8
 utonal
 36
16
 0-96-98-194-375
 1-11/9-10/7-7/4-9/8
 jove
 36
17
 0-96-192-194-375
 1-11/9-3/2-7/4-9/8
 jove
 36
18
 0-98-194-283-375
 1-10/7-7/4-5/4-9/8
 werckismic
 36
19
 0-192-194-283-375
 1-3/2-7/4-5/4-9/8
 otonal
 36
20
 0-96-98-286-375
 1-11/9-10/7-11/7-9/8
 jove
 36
21
 0-98-190-286-375
 1-10/7-9/7-11/7-9/8
 werckismic
 36
22
 0-101-190-286-375
 1-9/5-9/7-11/7-9/8
 werckismic
 36
23
 0-96-194-286-375
 1-11/9-7/4-11/7-9/8
 jove
 36
24
 0-98-194-286-375
 1-10/7-7/4-11/7-9/8
 werckismic
 36
25
 0-96-98-288-375
 1-11/9-10/7-11/6-9/8
 jove
 36
26
 0-98-190-288-375
 1-10/7-9/7-11/6-9/8
 jove
 36
27
 0-96-192-288-375
 1-11/9-3/2-11/6-9/8
 rastmic
 36
28
 0-190-192-288-375
 1-9/7-3/2-11/6-9/8
 jove
 36
29
 0-96-286-288-375
 1-11/9-11/7-11/6-9/8
 jove
 36
30
 0-98-286-288-375
 1-10/7-11/7-11/6-9/8
 jove
 36
31
 0-190-286-288-375
 1-9/7-11/7-11/6-9/8
 jove
 36
32
 0-96-192-194-471
 1-11/9-3/2-7/4-11/8
 jove
 45
33
 0-192-194-283-471
 1-3/2-7/4-5/4-11/8
 otonal
 45
34
 0-96-188-286-471
 1-11/9-11/10-11/7-11/8
 utonal
 45
35
 0-96-194-286-471
 1-11/9-7/4-11/7-11/8
 werckismic
 45
36
 0-96-188-288-471
 1-11/9-11/10-11/6-11/8
 utonal
 45
37
 0-96-192-288-471
 1-11/9-3/2-11/6-11/8
 rastmic
 45
38
 0-96-286-288-471
 1-11/9-11/7-11/6-11/8
 utonal
 45
39
 0-188-286-288-471
 1-11/10-11/7-11/6-11/8
 utonal
 45
40
 0-96-192-375-471
 1-11/9-3/2-9/8-11/8
 rastmic
 45
41
 0-96-194-375-471
 1-11/9-7/4-9/8-11/8
 jove
 45
42
 0-192-194-375-471
 1-3/2-7/4-9/8-11/8
 otonal
 45
43
 0-192-283-375-471
 1-3/2-5/4-9/8-11/8
 otonal
 45
44
 0-194-283-375-471
 1-7/4-5/4-9/8-11/8
 otonal
 45
45
 0-96-286-375-471
 1-11/9-11/7-9/8-11/8
 jove
 45
46
 0-194-286-375-471
 1-7/4-11/7-9/8-11/8
 werckismic
 45
47
 0-96-288-375-471
 1-11/9-11/6-9/8-11/8
 rastmic
 45
48
 0-192-288-375-471
 1-3/2-11/6-9/8-11/8
 rastmic
 45
49
 0-286-288-375-471
 1-11/7-11/6-9/8-11/8
 jove
 45

Hexads

Number
 Chord
 Transversal
 Type
 Complexity
1
 0-96-98-194-286-375
 1-11/9-10/7-7/4-11/7-9/8
 jove
 36
2
 0-96-98-286-288-375
 1-11/9-10/7-11/7-11/6-9/8
 jove
 36
3
 0-98-190-286-288-375
 1-10/7-9/7-11/7-11/6-9/8
 jove
 36
4
 0-96-188-286-288-471
 1-11/9-11/10-11/7-11/6-11/8
 utonal
 45
5
 0-96-192-194-375-471
 1-11/9-3/2-7/4-9/8-11/8
 jove
 45
6
 0-192-194-283-375-471
 1-3/2-7/4-5/4-9/8-11/8
 otonal
 45
7
 0-96-194-286-375-471
 1-11/9-7/4-11/7-9/8-11/8
 jove
 45
8
 0-96-192-288-375-471
 1-11/9-3/2-11/6-9/8-11/8
 rastmic
 45
9
 0-96-286-288-375-471
 1-11/9-11/7-11/6-9/8-11/8
 jove
 45